Results 41 to 50 of about 586 (91)

Determination of AdS Monopole Wall via Minimization

, 2019
In this note we solve a minimization problem arising in a recent work of Bolognesi and Tong on the determination of an AdS monopole wall. We show that the problem has a unique solution. Although the solution cannot be obtained explicitly, we show that it
Cao, Lei, Yang, Yisong
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A Fibering Map Approach for a Laplacian System With Sign-Changing Weight Function [PDF]

, 2014
We prove the existence of at least two positive solutions for the Laplacian system(E?)On a bounded region by using the Nehari manifold and the fibering maps associated with the Euler functional for the ...
Kazemipoor, Seyyed Sadegh, Zakeri, Mahboobeh   +1 more
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Groundstates of the Choquard equations with a sign-changing self-interaction potential

, 2018
We consider a nonlinear Choquard equation $$ -\Delta u+u= (V * |u|^p )|u|^{p-2}u \qquad \text{in }\mathbb{R}^N, $$ when the self-interaction potential $V$ is unbounded from below.
Battaglia, Luca, Van Schaftingen, Jean
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Quantitative Properties on the Steady States to A Schr\"odinger-Poisson-Slater System [PDF]

, 2014
A relatively complete picture on the steady states of the following Schr$\ddot{o}$dinger-Poisson-Slater (SPS) system \[ \begin{cases} -\Delta Q+Q=VQ-C_{S}Q^{2}, & Q>0\text{ in }\mathbb{R}^{3}\\ Q(x)\to0, & \mbox{as }x\to\infty,\\ -\Delta V=Q^{2}, & \text{
Xiang, Changlin
core  

Hylomorphic solitons on lattices

, 2010
This paper is devoted to prove the existence of solitons on lattices. We are interested in solitary waves and solitons whose existence is related to the ratio energy/charge. These solitary waves are called hylomorphic.
Benci, Vieri, Fortunato, Donato
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Ground States for a nonlinear Schr\"odinger system with sublinear coupling terms

, 2015
We study the existence of ground states for the coupled Schr\"odinger system \begin{equation} \left\{\begin{array}{lll} \displaystyle -\Delta u_i+\lambda_i u_i= \mu_i |u_i|^{2q-2}u_i+\sum_{j\neq i}b_{ij} |u_j|^q|u_i|^{q-2}u_i \\ u_i\in H^1(\mathbb{R}^n)
Oliveira, Filipe, Tavares, Hugo
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Existence and properties of soliton solution for the quasilinear Schrödinger system

Open Mathematics
In this article, we consider the following quasilinear Schrödinger system: −εΔu+u+k2ε[Δ∣u∣2]u=2αα+β∣u∣α−2u∣v∣β,x∈RN,−εΔv+v+k2ε[Δ∣v∣2]v=2βα+β∣u∣α∣v∣β−2v,x∈RN,\left\{\begin{array}{ll}-\varepsilon \Delta u+u+\frac{k}{2}\varepsilon \left[\Delta \hspace{-0 ...
Zhang Xue, Zhang Jing
doaj   +1 more source

Ground states and multiple solutions for Hamiltonian elliptic system with gradient term

Advances in Nonlinear Analysis, 2020
This paper is concerned with the following nonlinear Hamiltonian elliptic system with gradient ...
Zhang Wen, Zhang Jian, Mi Heilong
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Moser-Trudinger inequalities for singular Liouville systems

, 2015
In this paper we prove a Moser-Trudinger inequality for the Euler-Lagrange functional of a general singular Liouville system. We characterize the values of the parameters which yield coercivity for the functional and we give necessary conditions for ...
Battaglia, Luca
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Normalized solutions for the Choquard equations with critical nonlinearities

Advances in Nonlinear Analysis
This study is concerned with the existence of normalized solutions for the Choquard equations with critical nonlinearities −Δu+λu=f(u)+(Iα∗∣u∣2α*)∣u∣2α*−2u,inRN,∫RN∣u∣2dx=a2,\left\{\begin{array}{l}-\Delta u+\lambda u=f\left(u)+\left({I}_{\alpha }\ast ...
Gao Qian, He Xiaoming
doaj   +1 more source